Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Nonconvex quadratic programs, linear complementarity problems, and integer linear programs

  • Mathematical Programming
  • Conference paper
  • First Online:
5th Conference on Optimization Techniques Part I (Optimization Techniques 1973)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3))

Included in the following conference series:

Abstract

The problem of nonconvex quadratic programs is considered, and an algorithm is proposed to find the global minimum, solving the correspon ding linear complementarity problem. An application to the general complementarity problem and to 0–1 integer programming problems, is shown.

Research supported by National Groups of Functional Analysis and its Applications of Mathematical Commitee of C.N.R.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. -ABADIE J., On the Khun-Tucker Theorem. In "Nonlinear programming", J.Abadie (ed.), North-Holland Publ. Co., 1967, pp. 19–36.

    Google Scholar 

  2. -BEALE E.M.L., Numericae Methods. In "Nonlinear Programming", J.Aba die (ed.), North-Holland Publ. Co., 1967, pp. 133–205.

    Google Scholar 

  3. -BURDET C.A., General Quadratic Programming. Carnegie-Mellon Univ. Paper W.P.-41-71-2, Nov. 1971.

    Google Scholar 

  4. -COTTLE R. W., The principal pivoting method of quadratic programming. In "Mathematics of the decision sciences, Part I, eds. G.B.Dantzig and A.F.Veinott Jr. American Mathematical Society, Providence, 1968, pp. 144–162.

    Google Scholar 

  5. -COTTLE R.W. and W.C. MYLANDER, Ritter's cutting plane method for nonconvex quadratic programming. In "Integer and nonlinear programming", J;Abadie (ed.), North-Holland Publ. Co., 1970, pp.257–283.

    Google Scholar 

  6. -DANTZIG C.B., Linear Programming and Extension. Princeton Univ. Press, 1963.

    Google Scholar 

  7. -DANTZIG G.B., A.F. VEINOTT, Mathematics of the Decision Sciences. American Mathematical Society, Providence, 1968.

    Google Scholar 

  8. -EAVES B.C., On the basic theorem of complementarity. "Mathematical Programming", Vol.1, 1971, n. 1, pp.68–75.

    Article  Google Scholar 

  9. -GIANNESSI F., Nonconvex quadratic programming, linear complementarity problems, and integer linear programs. Dept. of Operations Research and Statistical Sciences, Univ. of PISA, ITALY. Paper A/1, January 1973.

    Google Scholar 

  10. -KARAMARDIAN S., The complementarity problem. "Mathematical Programming", Vol.2, 1972, n. 1, pp. 107–123.

    Article  Google Scholar 

  11. -KUHN H.W. and A.W. TUCKER, Nonlinear programming. In: "Second Berkeley Symp. Mathematical Statistics and Probability", ed. J. Neyman, Univ. of California Press, Berkeley, 1951, pp.481–492.

    Google Scholar 

  12. -LEMKE C.E., Bimatrix Equilibrium Points and Mathematical Programming. "Management Science", Vol.11, 1965, pp.681–689.

    Google Scholar 

  13. -RAGHAVACHARI M., On connections between zero-one integer programming and concave programming under linear constraints.

    Google Scholar 

  14. -RITTER K., A method for solving maximum problems with a nonconcave quadratic objective function. Z.Wharscheinlichkeitstheorie, Vern. Geb. 4, 1966, pp. 340–351.

    Google Scholar 

  15. -TOMASIN E., Global optimization in nonconvex quadratic programming and related lields. Dept. of Operations Research and Statistical Scien ces, Univ. of Pisa, September 1973.

    Google Scholar 

  16. -TUI HOANG, Concave programming under linear constraints. Soviet Math., 1964, pp.1437–1440.

    Google Scholar 

  17. -ZWART P.B. Nonlinear programming: Counter examples to global optimization algorithms proposed by Ritter and Tui. Washington Univ., Dept. of Applied Mathematics and Computer Sciences School of Ingeeniring and Applied Science. Report No. Co-1493-32-1972.

    Google Scholar 

  18. -BURDET The lacial decomposition method. Graduate School of Industrial Administration Carnegie Mellon Univ. Pittsbrgh, Penn. May 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Operations Research and Statistical Sciences, Univ. of PISA, Via S. Giuseppe, 22, Pisa, Italy

    F. Giannessi

  2. Mathematical Institute, Ca' Foscari University, Venice, Italy

    E. Tomasin

Authors
  1. F. Giannessi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Tomasin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

R. Conti A. Ruberti

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Giannessi, F., Tomasin, E. (1973). Nonconvex quadratic programs, linear complementarity problems, and integer linear programs. In: Conti, R., Ruberti, A. (eds) 5th Conference on Optimization Techniques Part I. Optimization Techniques 1973. Lecture Notes in Computer Science, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06583-0_43

Download citation

  • DOI: https://doi.org/10.1007/3-540-06583-0_43

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06583-8

  • Online ISBN: 978-3-540-37903-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation